Calculator for Expected Utility of Founding a Startup

Summary

This page provides a calculator that allows you broadly to compare the earning-to-give potential of a startup compared with a regular salaried job. The parameters are flexible so that you can make your own assumptions and perform sensitivity analysis. Given default parameters, founding a startup has slightly higher expected altruistic utility per hour than salaried work even after accounting for hours worked, diminishing marginal value of donated dollars, and modesty about your talents, but the difference between salaried employment and startup founding is not huge, and the calculation can easily favor salaried work under other plausible input assumptions. Obviously there are many other perspectives from which to approach the choice of salary vs. startup, and the calculation presented here is just one. The numbers in this calculator are based only on a single dataset and calculation framework and so should be taken with caution.

Here are the results of the calculator given the current parameter settings:

Probably most of the variation in results from person to person using this calculator will come from different risk tolerances. If you plan to donate to mainstream causes with relatively high room for more funding, entrepreneurship will look more promising than the default parameters make it seem.

These numbers should also be compared with earnings in finance and at companies with huge donation-matching programs.

Introduction

In 2012, Carl Shulman published a seminal blog post in effective-altruism circles: "Salary or startup? How do-gooders can gain more from risky careers". It drew upon the 2007 paper "The Incentives to Start New Companies: Evidence from Venture Capital" by Robert E. Hall and Susan E. Woodward, which estimated (Table 5, p. 19) an expected exit per startup of $9.2 million in 2006 dollars. "The median time from first venture funding to exit" was 49 months (Hall and Woodward 2007, p. 20).

This number is impressive, but it has a few limitations:

1. It assumes a founder already has venture funding.
2. It assumes a founder is a random sample from the set of all founders with funding, whereas you may know with reasonable certainty that, e.g., you're not as talented as the very best startup founders.
3. It ignores the fact that even altruists should generally be risk averse to some degree.

The current essay aims to address these shortcomings by providing a flexible calculator that takes these factors into account. My general approach is described in the following text, but to see the exact formulas, view the source of this web page and search for the JavaScript function calculate.

Data on startup exits

Hall and Woodward have a newer paper, "The Burden of the Nondiversifiable Risk of Entrepreneurship" (2010). I took my data from this paper rather than the 2007 one, though the numbers aren't that far apart. The startups in the data set "are mainly in information technology and biotechnology" (p. 1163).^a Figure 2 (p. 1172) of Hall and Woodward (2010) presents probabilities of startup exits of various sizes, which became the first and third columns of the below table. The exit values are pre-tax (Woodward, personal communication, 20 Nov. 2015). The second column represents my own made-up guesses about what point estimate within the exit-value ranges would be most representative of all the outcomes in the range. My point estimates are usually less than the middle of the ranges because the probability of a given exit presumably decreases almost monotonically with bigger exit values. You can modify these point estimates, and doing so will change the numbers in the results table.

The raw expected exit outcome based on the above table is $ million.^b If we set the point estimates to be the left end of each histogram bucket, the expected value is $8.01 million. This is still bigger than the per-entrepreneur payout that Hall and Woodward (2010) report in their Abstract: "We find that the typical venture-backed entrepreneur received an average of $5.8 million in exit cash." It seems that the exit values in Figure 2 are per-startup averages, which would explain why per-entrepreneur amounts would be about half that magnitude (assuming that a typical founding team size is 2, with some teams of size 1 and some of size 3 or more).^c

Even though Hall and Woodward (2010) say in their paper's abstract that the risk-neutral per-entrepreneur payout is $5.8 million, I think this falls a little short of the actual value. The reason is that, according to Table 3 (p. 1178), $5.8 million is the "certainty equivalent" for a risk-neutral founder relative to the possibility of earning $300K/year pre-tax at a normal job. The "certainty-equivalent value of the entrepreneurial opportunity [is] the amount that a prospective entrepreneur would be willing to pay to become a founder of a venture-backed startup" (p. 1164). In other words, for a risk-neutral entrepreneur:

Table 3 says the certainty equivalent would be $5.1 million if the startup founder had instead been earning a regular salary of $600K/year. This is $0.7 million less than if she had been earning $300K/year. So it should roughly be the case that the certainty equivalent if she had been earning $0/year is $5.8 million + $0.7 million = $6.5 million.^d

However, I think(?) Hall and Woodward (2010) also assume that the startup founder gets paid a salary: "We assume [...] a venture salary w equal to the posttax value of $150,000, postventure compensation w^* equal to the posttax value of $300,000" (p. 1176). I'll assume the salary is mostly at the $150K level, since my impression is that most of the relevant time periods are during rather than after the startup exits. The present value of a $150K salary over 4 years assuming the salary is paid at the end of each year^e is $532K using a 5% discount rate. I'll subtract this from the $6.5 million calculated above, which leaves about $6 million of pure equity expected present value. The reason to subtract out salary is that salary is paid with certainty, whereas the startup exits are highly variable, and I don't want to do the calculation as if the salary is also highly risky. I'll add back a salary for the entrepreneur later.

All of these numbers are pre-tax (Woodward, personal communication, 24 Nov. 2015). However, if you're donating your startup equity to tax-eligible charities, you can in principle pay no tax on it. So I'll consider the $6 million equity expected value an after-tax amount as well.

Now, in order to turn per-startup exit values from the above table into per-entrepreneur exit values, my calculator multiplies the exit outcomes as shown in the table above by ($6 million)/($ million) = . This adjustment assumes that there's no correlation between exit size and number of founders per team,^f while Hall and Woodward (2010) found that there was a nontrivial correlation (p. 1169). I ignore this issue for simplicity.

My calculator implicitly assumes that your equity share of your future startup will be something close to the average equity share across entrepreneurs. If you know your particular equity share, you could compare it against an average equity share based on Table 1 (p. 1169) of Hall and Woodward (2010) and adjust the estimates in this calculator up or down accordingly. That said, looking at the average equity share in Table 1 isn't a perfect way to do this comparison because there was a correlation between exit size and number of founders.

Risk-aversion parameters

Since most altruists should be somewhat risk-averse regarding gambles for large amounts of money, we should add parameters to specify how much the value of marginal dollars declines with increased wealth. The following table specifies a piecewise-linear utility function in which marginal dollars above the cutoff value of existing wealth but below the next cutoff value of existing wealth are worth a given fraction as much as a marginal dollar given no wealth. For example, given the current settings in the table, earning $20 million would be worth million times more than earning $1, because

Hall and Woodward (2010) also present risk-averse expected utilities, but they only discuss constant coefficients of relative risk aversion of ~0 to ~3. My input table above allows for a much more flexible (and intuitive) specification of a utility function.

Hours worked, inflation, etc.

The following table lists some additional parameters needed to calculate the expected utility of a venture-backed startup exit.

For a dollars-per-hour calculation, we need to know how long it takes the startup to exit. Hall and Woodward (2010) actually provide the full joint distribution of exit amounts and times to exit (Table 2, p. 1172), but I thought this would be too complicated to incorporate, and as noted in the appendix, it may make more sense to divide expected dollars by expected hours rather than calculate the expected value of dollars per hour over individual founder outcomes. Anyway, there's not an overwhelming correlation between startup exit value and time to exit, although there is a nontrivial correlation (Figure 3, p. 1173). One might think that failed startups tend to exit soon, which would reduce the opportunity cost of failure. But in fact, Hall and Woodward (2010) report a "negative correlation of lifetime and exit value" (p. 1171).

Hall and Woodward (2010) report regarding exit times (p. 1174): "The median is somewhat above four years. We do not calculate a mean lifetime, because the mean is sensitive to the extreme values, which are difficult to measure." I care most about the mean rather than the median, since I'm trying to calculate expected payoff divided by expected hours. The distribution is surprisingly uniform (Figure 5, p. 1174), so there shouldn't be a huge difference between median and mean. I approximate the mean using data from Table 2, p. 1172 as follows:

Here I'm using "12" as a guessed point estimate for the "10+" category, while for all other categories, I use the midpoint of the range.

Annual salaries of startup founders vary widely, but I chose a default value of $50K after tax for all years working on the startup—both before and after venture funding. In early years, especially before venture funding, founders may earn little or nothing, while in later years some earn six figures, so $50K is some kind of average of those two.

As Michael Dickens notes, many people are very talented but can guess that they aren't going to be the next Bill Gates or Mark Zuckerberg. To account for this, I include a dampening multiplier which says that when considering per-startup exit payoffs over $50 million, multiply the payoff amount by that multiplier (the default is 0.7) to account for the fact that you know you're not at the very top of the talent rankings. Of course, startup success also involves a lot of luck, which is why this multiplier shouldn't be set too close to 0. There's no precise way to set this parameter, but I thought it was important to include, because the estimates of startup expected utility would be unrealistically high without it. Of course, if you think you are the next Bill Gates, then you should set this parameter higher than 1 to account for the fact that you're more able to succeed than the average founder with venture funding.

I use a 5% real^g discount rate for the time value of money for two reasons:

1. The altruistic projects you would be funding may, in many cases, return somewhat more than the stock market, which many people expect to have something like a 3% real rate of return over the coming years.
2. 5% is the real discount rate used by Hall and Woodward (2010) when calculating the $5.8 million certainty equivalent^h, so I use the same rate to be consistent with their calculations.

You can't vary this parameter because the Hall and Woodward (2010) certainty equivalent assumes it's set at 5%. But heuristically, you can see that if you have a higher discount rate than this, entrepreneurship looks somewhat less favorable because most of the payout is many years away.

The Hall and Woodward (2010) figures are all in 2006 dollars adjusted by the Consumer Price Index (CPI). I bring them to 2015 dollars also using the CPI. The average CPI in 2006 was 201.6, while the CPI in Sep. 2015 was 237.945. This gives a ratio of 237.945/201.6 = 1.18.

I assume the founder works 50 weeks per year.

Time to get venture funding

As Ryan Carey (2014) and Chris Hallquist (2014) have noted, a main limitation of the Hall and Woodward analysis is that it starts from the point when a founder gets venture capital. But what are the odds of that happening, and how long does it take?

Carey (2014) estimated that roughly 0.2% to 4% of those seeking venture funding get it. This strikes me and Hallquist (2014) as too low. The acceptance rate to Y Combinator is 2.5% of applications, and it seems like most of those probably go on to get venture funding, based on the fact that of Y Combinator's "735 companies since 2006, 68% are still active, 20% have failed and 12% have been acquired." Given that Y Combinator is the most elite accelerator, the total proportion of applicants getting venture funding from somewhere (if not a top VC firm) is probably higher? And since I'm assuming the target readers of this piece are people who could get into Google, Microsoft, etc., their chances of getting into Y Combinator would probably be several times the typical rate. Overall, I've chosen 30% as my probability that a startup gets initial venture funding, though this is just a guess.

Carey (2014) also estimates that it takes months to years to develop a startup that has a good shot at venture funding. This agrees with my limited experience as a former employee of a pre-funding startup. I chose 1.5 years as an average length of time it takes to apply for initial venture funding.

For simplicity, I follow Hallquist (2014) in assuming that chances of getting funding are independent from one try to the next, so that the expected time to achieve venture funding is just (years to apply)/(probability of getting initial funding). In practice, one's getting initial funding is far from independent from one attempt to the next, because you might be exceptionally good or exceptionally bad at it. If you don't want to assume independence between trials, feel free to calculate an expected time until funding in some other way and then configure the parameters in the below table such that (years to apply)/(probability of getting initial funding) equals that number of years.ⁱ

Salaried pay

For comparison against a startup's $/hour, I also calculate the $/hour that one can earn as a non-founder employee, based on the following parameters:

The startup $/hour calculation divides the expected present value of future earnings over many years by the expected hours worked during those years. Because I'm discounting future wealth to adjust for the time value of money, while I'm not discounting hours worked, earnings further into the future decrease the stated $/hour number. Therefore, to put the $/hour figure for salaried work on equal footing with the startup-founder $/hour figure, I consider an employee who works at the salaried job for the same number of years as the expected time to exit for the startup founder. This stream of salary payments is time-discounted as well, so that the $/hour figure is a discounted present value divided by (undiscounted) hours worked, just as in the startup case.^k

Note that in general, employees at startups don't earn more in expectation (and might even earn less) than employees at big companies. Startup founders take an outsized share of the pie from a successful startup.

Comparison with net worth of Stanford entrepreneurs

Using an entirely different methodology, this post estimates "that the mean net worth of a Stanford alumnus who founded a corporation is $10.8 million as of 2013." (I assume net worth measures after-tax dollars, just like the other numbers in this piece.)

My adjustment to the calculation by Hall and Woodward (2010) suggests that an entrepreneur could earn $6.5 million (equity + salary, in 2006 dollars) in an average of ~4.5 years, and assuming it takes 5 years to successfully get venture funding, then an entrepreneur earns an average of ~$680K/year and so could earn an average of $10.8 million in ~16 years (ignoring inflation between 2006 and 2013 dollars). Presumably those answering the Stanford alumni survey had been working for more than 16 years on average, so we might expect their net worth to be higher than $10.8 million based on Hall and Woodward (2010), but (a) probably many of them weren't serial entrepreneurs and so didn't do entrepreneurship for all their working years^l, and (b) net worth is lower than earnings due to spending money. On the flip side, former entrepreneurs' net worth might have been higher than the (inflation-adjusted) exit values of their startups due to investment returns. So all told, the Stanford data agree pretty well with Hall and Woodward (2010), though there are reasonably big error bars with the comparison.

Considering the direct value of your startup

This piece has focused only on the earning-to-give potential of startup vs. salaried employment, but one should also consider the direct effects of one's work.

It's often suggested that a person's compensation roughly tracks the magnitude of that person's impact on society. This is not true in general—e.g., nonprofit employees have more social impact than their salaries suggest, Wikipedia contributors have no salary but nontrivial social impact, and so on. But it's plausible that within the business world, a company with a 10 times bigger valuation has at least several times the social impact in the typical case. Insofar as founding a startup creates more expected risk-neutral wealth than working at a salaried job, we should expect entrepreneurs to have more social impact in expectation.

However, a big caveat is that it's unclear whether that social impact is positive or negative! The sign of the impact of your startup depends on your specific industry and your views on differential progress. For example, I would guess that a computer-hardware startup has a pretty negative expected impact, because society would be better off if computing power arrived slower so that people would have more time to prepare for artificial general intelligence.

Depending on what specific domain your startup works in, the social effects of your business may either significantly increase or significantly decrease the overall estimate of your altruistic impact.

Appendix: Calculating $/hour

To calculate $/hour in this piece, I divide (expected dollars)/(expected hours). Dividing by an expected value is often hinky, since the expected value of a fraction is not the fraction of expected values. But in this case, a ratio of expected values seems to make more sense.

To see this, imagine that a large number N of people try entrepreneurship. They earn payouts P_i drawn from some distribution, and doing so takes times T_i, drawn from some other distribution. Any given person i finds herself earning P_i/T_i dollars per hour. But across the whole team of people, the payout is (Σ_i P_i) / (Σ_i T_i) = [ (Σ_i P_i)/N ] / [ (Σ_i T_i)/N ], i.e., (approximately) the ratio of expected values (for large N). This would be the relevant metric to assess if, for example, you were 80,000 Hours trying to advise all N people collectively to either try entrepreneurship or stick to a salaried jobs.

Even if you're just an individual making the decision, I still think a ratio of expected values is the better metric. Here's another example to illustrate. Suppose I offer you the following deal. I'll flip a coin. If it comes up heads, all you have to do is tell me "thank you" (which takes 1 second), and I'll give you $100. If the coin comes up tails, you have to do 100 hours of work for me, after which you'll get $100. You have to decide whether to take the deal before the coin flip, and you have to follow through on it to the end no matter what. Do you accept? You shouldn't. It's a bad deal, because the expected payout is $100, and the expected time cost is (100 hours + 1 second), giving a $/hour ratio of essentially $1/hour. If you had instead calculated the expected value of $/hour over the two scenarios, the result would have been 0.5 * ($100 / 0.0002778 hours) + 0.5 * ($100 / 100 hours) = $180,000/hour! Of course, if you could abandon the deal once the coin came up tails, then this would be a great deal. But startup founders need to invest many years before they can see whether the "coin" came up heads or tails, so to a reasonable approximation, they also can't renege on the deal.

Footnotes

1. Since most of the people reading this piece are probably considering software startups, it would be ideal if we had numbers purely for that sector. Table 4 on p. 1181 of Hall and Woodward (2010) gives some information about this. Biotech startups have higher certainty-equivalent values than software startups for significantly risk-averse entrepreneurs (compare line 3 vs. line 2). But p. 1180 notes: "For the less risk-averse entrepreneurs in the top wealth category, the value [of software startups] is higher [than for venture-backed companies in general], reflecting the disproportionate role of IT in the most successful startups, such as Google."  (back)
2. This is fairly close to the $9.2 million from Hall and Woodward (2007).  (back)
3. Hall and Woodward (2010), p. 1164: "About a quarter of entrepreneurs do not share the proceeds with other entrepreneurs; they operate solo. Another quarter share the entrepreneurial role equally with another founder. In the remaining cases, entrepreneurial ownership is distributed asymmetrically between a pair of entrepreneurs, or there are three or even more entrepreneurs."  (back)
4. This isn't exact because of taxes: $300K/year is worth slightly more than half of $600K/year in after-tax terms because of progressive tax rates. Also, for some reason, $0.7 million per year is less than what I calculate as the present value of $300K/year paid out over 49 months of startup founding, which should be around $1.1 million at a 5% annual discount rate and assuming the salary is paid monthly. I'm not sure why there's a discrepancy, but the numbers are close enough that it probably doesn't matter too much.  (back)
5. Hall and Woodward (2010), p. 1179: "we assume, for simplicity, that the entrepreneur receives the salary at the end of each year".  (back)
6. To see why, consider the following simple example. Suppose that half of startups exit with $1 million and half with $2 million. And suppose that all $1 million startups have a single founder, while all $2 million startups have two founders. Then the average per-entrepreneur payout would be $1 million. The expected per-startup payout would be (0.5)($1 million) + (0.5)($2 million) = $1.5 million. But it would not be the case that per-entrepreneur payouts are, each with 50% probability, (1/1.5) * ($1 million) and (1/1.5) * ($2 million).  (back)
7. The reason to use a real rather than a nominal rate is because this entire analysis ignores inflation. Doing so is fine as long as we assume that salaries, startup exit values, and the altruistic buying power of money all inflate at equal rates over time. For example, if inflation is 2.5% per year, then an exit 4 years from now is worth (1.025)⁴ times what I calculate here, but those dollars can only buy 1/(1.025)⁴ as much value.  (back)
8. From p. 1177: "The first three lines take the entrepreneur to be risk neutral, so the values are just present values at the five-percent annual real discount rate."  (back)
9. Of course, insofar as getting funding is not independent from one try to the next, there's value of information from trying once to see how good you are, and if you're extremely bad, you can stop trying, thereby saving opportunity cost. I haven't factored in value of information to this analysis.  (back)
10. When factoring in taxes, keep in mind that if you donate at least half of your income, your taxable income is ~half of your actual pre-tax income. For example, if your salary at Google is $200K/year, and if you donate at least $100K/year, you only get taxed as if you earned ~$100K/year.  (back)
11. I suppose I could have discounted hours worked as well, since if time = money and money is discounted, time should also be discounted. But I didn't choose to do that.

    By the way, if you set "Probability of getting venture funding on a given attempt" very low or "Years to figure out if you can get venture funding on a single attempt" very high, then the total years before successful startup exit will be large, and therefore, the companion number of years of salaried work will also be large. As a result, the $/hour for salaried work will decrease, because more of those years are further into the future and are therefore discounted more. Of course, in practice, you'd probably earn raises faster than inflation at a salaried job, so this reduction in the present value of salaried earnings per hour over more years worked isn't fully realistic. For example, if your annual raise above inflation is 5%, then since we discount at an annual real discount rate of 5%, a more correct calculation of the present value of your salaried earnings per hour would not change for increasing numbers of years worked. Alas, I haven't incorporated raises into this simple calculator.  (back)

12. Indeed, Table 2 on p. 25 of "Performance Persistence in Entrepreneurship" (2008) reports only 556 serial entrepreneurs out of 4,489 total in the "Internet and Computers" field, where "serial entreprenuers" are those who had previously founded a venture-backed company.  (back)